Explanation

(a) Current in a L-C-R series circuit,
$i = \frac{V}{\sqrt{R^{2} + \left( X_{L} - X_{C} \right)^{2}}}$
Where $\ V$ is rms value of current, R is resistance, $X_{L}$ is inductive reactance and $X_{C}$ is capacitive reactance.
For current to be maximum, denominator should be minimum which can be done, if
$X_{L} = X_{C}$
This happens in resonance state of the circuit
i.e, $\omega L = \frac{1}{\omega C}$
or $L = \frac{1}{\omega^{2}C}$ ...(i)
Given, $\omega = 1000s^{- 1},\ C = 10\mu F = 10 \times 10^{- 6}F$
Hence, $L = \frac{1}{(1000)^{2} \times 10 \times 10^{- 6}} = 0.1\ H = 100\ mH$